and the corresponding expression for left handed fermions is obtained from the transformation \(\mu _R\rightarrow \mu _L\) .
We use \(P\cdot V = p_0-\vec{p}\cdot \vec{v}\)  and
\(\vec{k}/\sqrt{k^2+m^2} \approx \hat{k} \equiv \vec{v}\)  since massless fermions are consistent with the hard loop approximation.
It is straightforward to modify the HTL integrals to the case of a QCD plasma by changing the QED coupling constant to the QCD one, and using [1]}
\(&& n(k)+\bar{n}(k) \rightarrow \frac{N_f}{2}(n_q(k)+\bar{n}_q(k)) + N_c n_g(k) \nonumber \\&& n(k)-\bar{n}(k) \rightarrow \frac{N_f}{2}(n_q(k)- \bar{n}_q(k))\) 
